In an electric motor, a circular coil with 100 turns of radius 2.0 cm can rotate between the po

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In an electric motor, a circular coil with 100 turns of...

In an electric motor, a circular coil with 100 turns of radius $2.0 \mathrm{~cm}$ can rotate between the poles of a magnet. When the current through the coil is $75 \mathrm{~mA}$, the maximum torque that the motor can deliver is $0.0020 \mathrm{~N} \cdot \mathrm{m}$. (a) What is the strength of the magnetic field? (b) Is the torque on the coil clockwise or counterclockwise as viewed from the front at the instant shown in the figure?

In an electric motor, a circular coil with 100 turns of radius $2.0 \mathrm{~cm}$ can rotate between the poles of a magnet. When the current through the coil is $75 \mathrm{~mA}$, the maximum torque that the motor can deliver is $0.0020 \mathrm{~N} \cdot \mathrm{m}$.
(a) What is the strength of the magnetic field? (b) Is the torque on the coil clockwise or counterclockwise as viewed from the front at the instant shown in the figure?

Key Concepts

Coil Geometry and Area

The area A of the coil, especially when it is circular, plays a crucial role in calculating its magnetic dipole moment and the resultant torque in a magnetic field. For a circle, the area is A = ?r², emphasizing how the dimensions of the coil directly affect its electromagnetic behavior.

Right-Hand Rule

The right-hand rule is a technique used to determine the direction of vectors resulting from cross products, such as the torque on a current loop. By aligning the fingers with the magnetic dipole moment and curling them toward the magnetic field, the thumb points in the direction of the torque. This concept is essential for predicting the rotational behavior of the coil in devices like electric motors.

Torque on a Current Loop in a Magnetic Field

The torque experienced by a current loop in a magnetic field is given by the cross product ? = m × B, where m is the magnetic dipole moment and B is the magnetic field. This torque tends to rotate the loop to align its magnetic moment with the field, reaching a maximum when the loop is perpendicular to the field direction.

Magnetic Dipole Moment

This is a measure of the strength and orientation of a current-carrying loop’s magnetism. It is calculated as m = NIA, where N is the number of turns in the coil, I is the current flowing through it, and A is the area of the loop. Understanding the magnetic dipole moment is critical for predicting how the loop will interact with an external magnetic field.

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